Beluchenko's p13: Difference between revisions
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Beluchenko's p13 first appeared [[semi-natural]]ly in March {{year|2016}}, in a [[symmetric]] [[soup]] submitted to [[Catagolue]].<ref name="post29522" /> | Beluchenko's p13 first appeared [[semi-natural]]ly in March {{year|2016}}, in a [[symmetric]] [[soup]] submitted to [[Catagolue]].<ref name="post29522" /> | ||
==Variants== | == Variants == | ||
{{gallery top}} | {{gallery top}} | ||
{{gallery item|{{EmbedViewer | {{gallery item|{{EmbedViewer | ||
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{{gallery bottom}} | {{gallery bottom}} | ||
==LCM oscillators== | == LCM oscillators == | ||
The [[LCM oscillator]]s below are the smallest known ones of their period by population while satisfying the condition that at least one cell oscillates at the full period. | The [[LCM oscillator]]s below are the smallest known ones of their period by population while satisfying the condition that at least one cell oscillates at the full period. | ||
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* [[p39 pi-heptomino hassler]] | * [[p39 pi-heptomino hassler]] | ||
==References== | == References == | ||
<references> | <references> | ||
<ref name="post29522">{{LinkForumThread | <ref name="post29522">{{LinkForumThread | ||
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* {{LinkPentadecathlonObject|34P13.1}} | * {{LinkPentadecathlonObject|34P13.1}} | ||
{{Sparker|p=13|type=dot|strength=strong}} | {{Sparker|p=13|type=dot|strength=strong}} | ||
{{seminatural}} | {{seminatural}} | ||
__NOTOC__ | __NOTOC__ | ||
Revision as of 13:48, 7 August 2024
| Beluchenko's p13 | |||||||||
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| Pattern type | Oscillator | ||||||||
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| Number of cells | 34 | ||||||||
| Bounding box | 17 × 17 | ||||||||
| Period | 13 (mod: 13) | ||||||||
| Heat | 30.2 | ||||||||
| Volatility | 0.96 | 0.96 | ||||||||
| Kinetic symmetry | / | ||||||||
| Discovered by | Nicolay Beluchenko | ||||||||
| Year of discovery | 2009 | ||||||||
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Beluchenko's p13 is a period-13 oscillator found by Nicolay Beluchenko[1] on January 4, 2009.[2] In terms of its 34 cells, it is the smallest known period 13 oscillator.[3] It gives sparks, allowing for the construction of non-trivial higher-period oscillators as seen in a later section.
There are three ways in which two of these can share a common block, all of which are shown below. Jason Summers also discovered that four of these oscillators can be combined to create a statorless oscillator (i.e., where none of the cells are alive in all phases), making it the first such oscillator known with a prime period greater than two.
Beluchenko's p13 first appeared semi-naturally in March 2016, in a symmetric soup submitted to Catagolue.[4]
Variants
| Two copies of this oscillator sharing a block (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here |
| Two copies of this oscillator sharing two blocks (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here |
| Two copies of this oscillator sharing a block (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here |
| Four copies of this oscillator sharing four blocks (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here |
LCM oscillators
The LCM oscillators below are the smallest known ones of their period by population while satisfying the condition that at least one cell oscillates at the full period.
| p104 with figure eight (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here |
| p143 with p11 thumb (click above to open LifeViewer) Catagolue: here |
| p988 with p76 pi-heptomino hassler (click above to open LifeViewer) RLE: here Plaintext: here Catagolue: here |
See also
References
- ↑ New Oscillators at Game of Life News. Posted by Heinrich Koenig on January 08, 2009.
- ↑ Jason Summers' all-osc pattern collection. Retrieved on June 28, 2009.
- ↑ "Class 2 Objects Catalog". Retrieved on April 11, 2009.
- ↑ praosylen (March 31, 2016). Re: Soup search results (discussion thread) at the ConwayLife.com forums
External links
- Beluchenko's p13 at Adam P. Goucher's Catagolue
- 34P13.1 at Heinrich Koenig's Game of Life Object Catalogs
Categories:
- Patterns
- Oscillators with 34 cells
- Periodic objects with minimum population 34
- Patterns with 34 cells
- Patterns found by Nicolay Beluchenko
- Patterns found in 2009
- Patterns that can be constructed with 14 gliders
- Oscillators
- Oscillators with period 13
- Prime-period oscillators
- Oscillators with mod 13
- Oscillators with heat 30
- Oscillators with volatility 0.96
- Oscillators with strict volatility 0.96
- Oscillators with / symmetry
- Sparkers
- Sparkers with period 13
- Dot sparkers
- Strong sparkers
- Semi-natural periodic objects